I'd rather teach payback to it than crunch because-
Because crunch has base power of 85. Add STAB 127.5.
But in payback its base power is 50 but when the pokemon is hit (which tyranitar usually is because of its slow speed) the moves power double therefore becoming 100 and then add STAB it would be 150.

This set gives him enough speed to out-run Politoed and if you run Jolly Ninetales. Stone-edge is STAB. Crunch is strong STAB while Pursuit is strategic STAB too hurt a fleeing Poltoed/Ninetales. Earthquake is for coverage. Thunder-punch is coverage specifically for destroying Poltoed the arch-nemesis of Tyranitar.

Swagger- Basically a set-up for something unexpected.Foul Play- A new move that uses the foes' base Atk, the move acts as if the target is attacking themselves, and thus is more powerful when the opponent has higher Attack, it is amplified by Swagger thus not making you all that threatened because of confusion, and STAB.Equake- No reason needed. This skill is OP.Ice Punch, Fang/Rock Slide/Aerial Ace- Ice to deal with weaknesses, Rockslide helps and has a chance of flinching or Aerial Ace a move that never misses. Your choice, as for me, I currently use Rockslide I feel lucky with that flinch.

My Tyranitar is a good somewhat defensive sweeper. It can take hits while it builds speed, then it can stop opponents in their tracks. It does get annoying though, because everyone keeps forfeiting. Here's what mine knows.

Tyranitar-Adamant Nature: +Atk,-SAtkEVs: 252Atk, 50Spd, 108Def, 100SDefItem: Sitrus Berry (good for surviving longer, and Tyranitar's defensive stats help)Ability: Sand Stream (ensures they don't survive with focus sash)Moves:
-Rock Polish: raises speed 3 levels-Rock Slide: hits 2 people in double or triple, more accurate than stone edge, and can make them flinch (works well with rock polish)-Fire Fang: type coverage(bug, steel, grass), burn (adds with sandstorm), and can flinch-Earthquake: because everyone needs a good power-move, but you can pick whichever else you like
p.s. One thing I've noticed is most people forget rock beats ice, but ice doesn't beat rock, so don't fear the ice types unless they know water attacks (yes, rock type attacks are still super effective on ice and water double types; no, fire fang is not). Also, tyranitar can learn ice fang and thunder fang too, so if you want more flinch moves, more status problems, or more type coverage(ice: beats ground, grass, flying; electric: beats water, flying), pick one of those.

My Tyranitar is a good somewhat defensive sweeper. It can take hits while it builds speed, then it can stop opponents in their tracks. It does get annoying though, because everyone keeps forfeiting. Here's what mine knows.

Tyranitar-Adamant Nature: +Atk,-SAtkEVs: 0Hp, 252Atk, 0Def, 0SAtk, 6SDef, 252SpdIVs: 31 on all except for 23SAtk and 10SpdItem: Sitrus Berry (good for surviving longer, and Tyranitar's defensive stats help)Ability: Sand Stream (ensures they don't survive with focus sash)Moves:-Rock Polish: raises speed 3 levels-Rock Slide: hits 2 people in double or triple, more accurate than stone edge, and can make them flinch (works well with rock polish)-Ice Fang: type coverage (grass, ground, flying, dragon), may freeze, may flinch-Earthquake: because everyone needs a good power-move, but you can pick whichever else you like

p.s. One thing I've noticed is most people forget rock beats ice, but ice doesn't beat rock, so don't fear the ice types unless they know water attacks (yes, rock type attacks are still super effective on ice and water double types; no, fire is not). Also, tyranitar can learn fire fang and thunder fang too, so if you want more flinch moves, more status problems, or more type coverage(fire: beats bug, grass, steel, ice; electric: beats water, flying), pick one of those. Also, I made an earlier post similar to this one, then I realized ice fang was better than fire fang because fire takes care of steel, bug, and grass. Earthquake covers steel and rock slide covers bug, and ice fang takes care of grass, ground, and those pesky dragon types. I hope this helps.

I agree with everything, but i'd rather have crunch over rock polish because of STAB and even more coverage over physics (even though they can't even hurt tyranitar).But I do like the rock polish idea, but i also like the 80 power +40 from STAB and 100 accuracy. But the flinching and speed boost can be a deadly combination, So i'd go with either moveset.

I would like to point out that in your comment you mentioned you prefer Crunch over Rock Polish because crunch makes others flinch. I am sorry to say that you are mislead. Crunch does not make them flinch. I believe you are thinking of Bite: a move with a power of 60, accuracy of 100, and the ability to make opponents flinch. If you want Crunch to make them flinch, simply give Tyranitar either a King's Rock or a Razor Fang item to hold. Those items will give a small chance of flinch to any move, and a bigger chance of flinch to moves that already have a chance to flinch. I would like to point out that I have a Bug type Scizor in my team and do not worry about Psychic types. Also, most psychic types have low Def and good SDef, so Tyranitar has them overpowered.

Allright If You Want To Have A But Kickin Tyranitar Then Make It Hold A Power Brasser, It Raises His Attack Up To Like 4 times more than the usual!! (The First Time He Leveled Up While Holding His Attack Gained 11!) But It Also Doesnt Give Him Much Speed But Hes Normally Not Fast So Yea. Next Give Him This Moveset:
Thunder Fang - For Water Types And Is Physical
Earthquake - Just Strong!
Stone Edge - Strong As Well!
Payback - Hes Gona Be Slow So He'll Go 2nd Everytime So The Power Will Double Making It Stronger Than Cruch

The power bracer does not increase a pokemon's attack stat, it makes a pokemon gain 4 attack EVs after every battle, but since you don't gain EVs from competitive battling, so it will only halve you seed stat.

I was able to pull together a very strategic moveset:
Tyranitar (M)
Nature: Adamant (+A,-SA)
EVs: ATTACKER!
Ability: Sand Stream
Moves:
Dragon Dance (+ 1 A, +1 S, and it corresponds with the strategy)
Ice Fang/Ice Punch (boosted by D.Dance and for type coverage)ASSURANCE (may not sound like much, but think... boosted by D.Dance, STAB, AND with Sand Stream kicked in, there's damage caused after the first turn DOUBLING the attack power of the move the next turn. 50/2 = 25 ..... 50+25=75 (STAB) x2 (effect) = 150 base damage! Also, the D.Dance # variation will boost even further!)
Earthquake (boosted by D.Dance and more type coverage)

-Dragon Dance: Raises Speed and Attack, so it'll be at a better advantage.
-Earthquake: Good move, for the most part.
-Ice Punch: Handles Flying and Grass, the two types that Earthquake won't get a hard hit on.
-Fire Punch/Aerial Ace/Crunch: The first two are for type coverage, and Crunch gives a powerful STAB move; either of those can come in handy.

I'd also recommend moves with pretty good accuracy, in general. Crazy powerful moves aren't all that good when they miss.